Question: Daniel is 20 years older than Kevin. Eleven years ago, Daniel was 5 times as old as Kevin. How old is Kevin now?
Solution: We can use the given information to write down two equations that describe the ages of Daniel and Kevin. Let Daniel's current age be $d$ and Kevin's current age be $k$ The information in the first sentence can be expressed in the following equation: $d = k + 20$ Eleven years ago, Daniel was $d - 11$ years old, and Kevin was $k - 11$ years old. The information in the second sentence can be expressed in the following equation: $d - 11 = 5(k - 11)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to use our first equation for $d$ and substitute it into our second equation. Our first equation is: $d = k + 20$ . Substituting this into our second equation, we get the equation: $(k + 20)$ $-$ $11 = 5(k - 11)$ which combines the information about $k$ from both of our original equations. Simplifying both sides of this equation, we get: $k + 9 = 5 k - 55$ Solving for $k$ , we get: $4 k = 64$ $k = 16$.